 Greetings and welcome to the Introduction to Astronomy. In this video, we are going to talk about time and the calendar. That's one of the basics of what astronomy, that was set up to do originally, was to be able to determine time and how we measure different parts of time, and to use as a calendar to be able to determine when the seasons would start and end. So let's go ahead and get started here. And what we find is that there are a number of different ways of measuring time, and the early astronomers used these as way of developing the calendar. And the calendar was all based on astronomical events. And what do we mean? We look at things like our day is based on the rotation of the Earth. How long it takes the Earth to rotate once on its axis gives us our day. A week, that's one that students sometimes ask about, how is a week related to astronomical observations? And why do we have seven days in a week and not eight or ten or five? And there were seven objects that move among the stars, and each day of the week is then named after one of those objects. So we have Sunday for the sun and Monday for the moon, and some of the others are not completely obvious, especially in English, but in other languages you can see that there are days for Mercury and Venus and Mars and Jupiter and Saturn. So that's why we have seven days in a week because the ancients identified seven objects that were special that did not move with the stars. Our month is based on the phases of the moon. The phases of the moon go through a 29 and a half day cycle, and that's very close to a typical month. So our month is based on phases of the moon, and a year is the revolution of Earth around the sun. So how long does it take the Earth to move around the sun? Well, that's 365 and a quarter days, and that gives us our year. So everything is set up this way, and why do we have such unusual numbers? Why are there odd numbers of weeks in a year and months in a year? And days, why does nothing work out? And that's because they're all based on different measurements. So there's no reason that there has to be a specific number of rotations of the Earth corresponding to a set of phases of the moon or a set of rotations of the Earth to revolutions around the sun. So that's why nothing comes out very even, and our calendar is the way it is. So let's look at a couple of these in a little bit more detail here, and what we can see is for the day, how do we measure a day? Well, there's a couple different measures that we can use. And in fact, we use, normally in everyday occurrence, we use the solar day, which is measured relative to the sun. Astronomers, on the other hand, use the sidereal day, which is relative to the stars. Now, why these are different is because if we look at the Earth's rotation, the Earth takes 23 hours and 56 minutes to rotate. However, our solar day, the day that we use, is 24 hours. So the difference between these two means that the positioning of the stars will change relative to the sun, and that's shown in the image over off to the right-hand side here. If we start at noon on one day where everything is lined up, the sun and a distant star here and the sun will be in a line and they would be in the same position out in the sky if we looked out to them. Now, if we let the Earth rotate one time and get back to what's pointing exactly the same direction out in space out to that distant star, we now find that the sun hasn't quite gotten back there yet. So after 23 hours and 56 minutes, the star will be back to where it started, but the sun won't quite be there. And that's because the Earth has moved a little ways around in the orbit around the sun. So because of that, it now takes just a little bit longer for the Earth to rotate to get the sun back to the same position and to get back to noon again. So because the Earth is moving around the sun, we get this difference between the solar day and the sidereal day. So astronomers would look at the sidereal day, how long it takes the stars to get back in position, but for ordinary civil time, we use the solar day. Now there's even different types of solar days because the solar day is not uniform. And what we can see is what we use is there's solar time and we can have apparent solar time, and this is what we would get from a sundial. That is where the sun is in the sky and that would change from day to day because the days would not be exactly the same by apparent solar time. The sun would be in different positions in the sky from day to day. And because of that, the apparent solar time or sundial time would not be the same. And that can vary by easily, you know, a half an hour over the course of the year. So the sun might get to its highest point at a certain time, but a little later in the year it might get to that highest point 15 or 20 minutes later. So it's not the same because the orbit of the earth around the sun is not uniform. So since we don't want days that are varied, that are varied, we use mean solar time. The mean solar day is exactly 24 hours and that is what we use as our ordinary day. Now we also divide the earth into time zones. So if you've traveled, you know that you can set your clocks. As you move further west, you will have to set your clocks backward. And if you move to the east, you have to set them forward and that's because you're changing the time zones. Their time zones are to minimize the amount of change that you have to do when traveling. And that is because normally if you look at apparent solar time, it would change by where you are. So two cities, even relatively close together, would have slightly different times based on apparent solar time, but we average together so that much of the eastern United States, whether you're in New York or in Detroit, they are both using eastern time. So the time is the same there and it's not until you travel a little further west, say to Chicago, where the time shifts back an hour to keep the daylight time matching up with the time, the civil time that we're used to. And we also mentioned, of course, daylight savings time here, which is not an astronomical event and is only done to shift the time. It doesn't change the, when it changes anything, it is just changed to give more sunlit hours in the evening. So instead of the sun rising earlier and setting earlier in the summertime, the sun will rise a little bit later and set a little bit later to push those sunlight hours into the evening. But it has no astronomical event, nothing to do astronomically, it is just a civil change in order to put those daylight hours into the evening time. So let's move on and see what else we can talk about here. So let's look a little bit, I mentioned this a little bit earlier, and because the times are determined by astronomical motions that are not related to each other, so they are not directly related to each other and this is important. So the day, the month, and the year, well, the average number of days in a month is 29.5306. So there are 29.5306 would be the number of days in the month based on the lunar cycle. The number of days in a year would be 365.2422. So what happens with these fractional values? They don't come out even if the lunar cycle was exactly 30 days, then we could set up months as being exactly 30 days. But then we'd also have the problem that there aren't an equal number of 30s in the year, so we wouldn't have an equal number of months in the year. So that's why we have uneven month lengths that we need different lengths of the month. So some have 30 and some have 31 days for two reasons, first of all, this is not an even amount. And secondly, it happens because there aren't an even number of months in the year, and there'd be an extra few days left over at the end of the year, so we have to put those days in somewhere and they just make each of the months a little bit longer. The leap years is the other one that we look at here and we want to talk about those a little bit, we'll talk about those a little bit more later, but this 365 and almost a quarter days is why we add a leap year almost every four years. And we'll look at that in a little bit more detail coming up, but first of all, let's look at some of the early calendars and we've talked about some of these, have been talked about in previous lectures. We'll talk about Stonehenge, and Stonehenge has alignments with the rising and setting of the sun and the moon, and especially at the solstices. Solstice occurs when the sun is either at its highest or lowest point. So the summer solstice is when the sun is highest in the sky and rises for this north of east and sets for this north of west. And in the winter solstice, the sun would be lowest in the sky and sets more south of east and sets south of west. So that looks at the moon, but other calendars looked at other objects. For example, the Mayans gave a very complex calendar based not on the sun or the moon, but on the planet Venus, which was the brightest star-like object in the sky and was very important in their calendar. The Chinese looked at the cycle of Jupiter. Jupiter has a 12-year cycle, which gives us the 12-year cycle of the Chinese zodiac. So you don't have to base calendars just on the sun or moon. Other cultures have used other objects, including Venus and Jupiter, to be able to make their calendars. Now to come back, and let's look a little bit about leap years that we started talking about earlier. Leap years, one of the earlier calendars, was the Julian Cant calendar, introduced by Julius Caesar, and what was done was to approximate the year as 365 and a quarter days. That's pretty close, if you remember. It was 365.2422, and that's pretty close to 365 and a quarter. So if you add a leap year every fourth year, then that would keep the calendar from shifting. So otherwise, you would be very quickly losing a quarter of a day each year. If you're only using 365 days, you're going to be off by a quarter of a year, and every four years that adds up to a day, so very quickly within a lifetime, you would notice the calendar shifting. The problem with the Julian calendar is that it does differ from the actual year by 11 minutes. Now 11 minutes isn't all that much. You're not going to notice it over the course of a lifetime. That 11 minutes a year, even times 100, you're only talking 1100 minutes, so it's not going to make a big, big difference over the course of a lifetime. But over long periods of time, and by 1582, it had come out to be 10 days. So that 11 minutes a year for 1500 years adds up and becomes 10 days. So spring was starting earlier and earlier, which was causing problems with the calendars as to when Easter would occur. So Easter was occurring earlier and earlier, and there were big problems with the calendar, so spring was starting earlier and earlier. And the problem would continue to grow. So this is something that had to be fixed, and it was fixed in 1582, and it was fixed by Pope Gregory XIII. And what Pope Gregory did is come up with the Gregorian calendar, which, first of all, did a few things. It dropped 10 days out of the year. So you had to get everything back into sync to where they were supposed to be. So those 10 days that had been slowly added into the year over the last 1500 years had to go someplace. So what was done was it was decreed that you'd have October 4th, and the next day would be October 15th, just to drop those 10 days to bring everything back into sync. However, the problem doesn't go away unless you fix the issue with leap years. So because another 1500 years later, we'd be right back where we started and would be 10 days off. So what was done was to change how the leap years worked. So what we kept was what the Julian calendar said was that every 4th year is a leap year, except century years would have to be divisible by 400. So years like 1700, 1800, and 1900, they are divisible by 4, but they are not divisible by 400. So these were not leap years. But 2000, which is divisible by both 4 and 400, is a leap year. So 2100 will not be a leap year. And that averages things out every 100 years or so, and keeps things pretty close into alignment. So the calendar no longer drifts near what it used to, and it will take many tens of thousands of years for it to begin to drift very far away. It's still not perfect again because there's not an exact number. So we have to keep approximating the number of days in a year and trying to get it as close as we can. So let's finish up, as we do with our summary. And what we look at here is that the day is based on the rotation of the Earth. So we've talked about that. But there is a difference of 4 minutes between the solar and sidereal day. And that is because the Earth is moving around the sun at the same time. So Earth orbiting the sun causes this change. I should qualify because this is something that sometimes comes up, that this has nothing to do with leap years. This is not where the leap year comes up. It has nothing to do with this. So cross that out. That 4 minutes has nothing to do with the leap years. This is only because of the average number of days in a year. It's not the difference between the solar and sidereal days. We look in that time is based on unrelated astronomical motions. So that's why there are not even number of days in a month or days in a year. Nothing comes out even because the astronomical motions are not related to each other. And then finally we've finished up and looked at leap years, so we have to adjust and keep the calendar from slowly shifting over time. So that completes this lecture on time and the calendar. We'll be back again next time for another topic in astronomy. So until then, have a great day, everyone, and I will see you in class.